Experimental Extraction of Coherent Ergotropy and Its Energetic Cost in a Superconducting Qubit

Abstract: Quantum coherence, encoded in the off-diagonal elements of a system's density matrix, is a key resource in quantum thermodynamics, fundamentally limiting the maximum extractable work, or ergotropy. While previous experiments have isolated coherence-related contributions to work extraction, it remains unclear how coherence can be harnessed in a controllable and energy-efficient manner. Here, we experimentally investigate the role of initial-state coherence in work extraction from a superconducting transmon qubit. By preparing a range of pure states and implementing three complementary extraction protocols, we reveal how coherence governs the partitioning of ergotropy. We find that the choice of initial state depends on the dominant decoherence channel-energy relaxation or dephasing. By further accounting for thermodynamic costs, we identify optimal initial states that maximize the efficiency. These results establish initial-state design as a practical and scalable approach to coherence control, offering guidance for the development of efficient quantum thermodynamic devices.